Optimal (Under-)Pricing and Allocation of Publicly Provided Goods

Abstract

This paper exploits the links between a private value distribution’s hazard rate, mean residual value, and eta functions in order to characterize posted-price rules for a public agency to allocate scarce units of an indivisible good under the utilitarian distributional objective of maximizing expected consumer surplus. Sufficient conditions on the monotonic and non-monotonic classes of the functions are established that identify either market assignment at the clearing price or lottery assignment with partial or complete under-pricing as the optimal allocation mechanism. The results are summarized across a wide range of parametric value distributions, and selected non-monotonic cases are evaluated numerically to determine the relative scarcity or abundance of the good necessary for market or non-market assignment to dominate.